(x-2)(x-8)=112

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Solution for (x-2)(x-8)=112 equation: 


Simplifying
(x + -2)(x + -8) = 112

Reorder the terms:
(-2 + x)(x + -8) = 112

Reorder the terms:
(-2 + x)(-8 + x) = 112

Multiply (-2 + x) * (-8 + x)
(-2(-8 + x) + x(-8 + x)) = 112
((-8 * -2 + x * -2) + x(-8 + x)) = 112
((16 + -2x) + x(-8 + x)) = 112
(16 + -2x + (-8 * x + x * x)) = 112
(16 + -2x + (-8x + x2)) = 112

Combine like terms: -2x + -8x = -10x
(16 + -10x + x2) = 112

Solving
16 + -10x + x2 = 112

Solving for variable 'x'.

Reorder the terms:
16 + -112 + -10x + x2 = 112 + -112

Combine like terms: 16 + -112 = -96
-96 + -10x + x2 = 112 + -112

Combine like terms: 112 + -112 = 0
-96 + -10x + x2 = 0

Factor a trinomial.
(-6 + -1x)(16 + -1x) = 0


Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

Subproblem 2
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {-6, 16}

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